Name: Class: Date: Unit 3: Stretching and Shrinking. Investigation 2: Similar Figures. Practice Problems
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1 Unit 3: Stretching and Shrinking Investigation 2: Similar Figures Practice Problems Directions: Please complete the necessary problems to earn a maximum of 7 points according to the chart below. Show all of your work clearly and neatly for credit- which will be earned based on completion rather than correctness. I can understand what it means for figures to be similar. Lesson Practice problems Options Maximum Points Lesson 1: Drawing Wumps (Making Similar Figures) Lesson 2: Hats Off to the Wumps (Changing a 1 1 Point 2, 3, 4, 5, 6, 7 3 Points Figure s Size and Location) Lesson 3: Mouthing Off and Nosing Around (Scale 8, 9, 10, 11, 12, 13 3 Points Factors) / 7 Points
2 1. The table below gives key coordinates for drawing Mug Wump s mouth and nose. It also gives rules for finding the corresponding points for four other characters- some members of the Wump family and some impostors. a. Before you find the coordinates or plot points, predict which characters are the impostors. b. Complete the table. Plot the figures on the grid paper. Label each figure.
3 c. Which of the new characters (Glum, Sum, Tum, and Crum) are members of the Wump family? Which are impostors? d. Choose one of the new Wumps. How do the mouth and nose measurements (side lengths, perimeter, area, angle measures) compare with those of Mug Wump? e. Choose one of the impostors. What are the dimensions of this impostor s mouth and nose? How do the mouth and nose measurements compare with those of Mug Wump? f. Do your findings in parts (b)-(e) support your prediction from part (a)? Explain. 2. a. Design a Mug-like character of your own on grid paper. Give your character eyes, a nose, and a mouth. b. Give coordinates so that someone else could draw your character.
4 c. Write a rule for finding coordinates of your character s family. Check your rule by plotting the figure. d. Write a rule for finding the coordinates of an impostor. Check your rule by plotting the figure. 3. a. On grid paper, draw triangle ABC with vertex coordinates A(0,2), B(6,2), and C(4,4) b. Apply the rule (1.5x, 1.5y) to the vertices of triangle ABC to get triangle PQR. Compare the corresponding measurements (side lengths, perimeters, areas, area, angle measures) of the two triangles. c. Apply the rule (2x, 0.5y) to the vertices of triangle ABC to get triangle FGH. Compare the corresponding measurements (side lengths, perimeters, areas, angle measures) of the two triangles. d. Which triangle, PQR or FGH, seems similar to triangle ABC? Why?
5 4. a. On grid paper, draw parallelogram ABCD with vertex coordinates A(0,2), B(6,2), C (8,6), and D(2,6) b. Write a rule to find the vertex coordinates of a parallelogram PQRS that is larger than, but similar to ABCD. Test your rule to see if it works. c. Write a rule to find the vertex coordinates of a parallelogram TUVW that is smaller than, but similar to, ABCD. Test your rule to see if it works. For Exercises 5 and 6, study the size and shape of the polygons below. 5. Multiple Choice Choose the pair of similar figures.
6 6. Find another pair of similar figures. Explain your reasoning. 7. Use the figures below to solve parts a, b, and c. a. Draw a figure similar, but not identical, to the rectangle. b. Draw a figure similar, but not identical, to the triangle. c. How do you know your scale drawings are similar to the given figures? 8. The diagram below shows two similar polygons. a. Write a rule for finding the coordinates of a point on Figure B from the corresponding point on Figure A. b. Write a rule for finding the coordinates of a point on Figure A from the corresponding point on Figure B.
7 c. i. What is the scale factor from Figure A to Figure B? ii. Use the scale factor to describe how the perimeter and area of Figure B are related to the perimeter and area of Figure A. d. i. What is the scale factor from Figure B to Figure A? ii. Use the scale factor to describe how the perimeter and area of Figure A are related to the perimeter and area of Figure B. 9. a. Suppose you make Figure C by applying the rule (2x, 2y) to the points on Figure A from Exercise 8. Find the coordinates of the vertices of Figure C. b. i. What is the scale factor from Figure A to Figure C? ii. Use the scale factor to describe how the perimeter and area of Figure C are related to the perimeter and area of Figure A? c. i. What is the scale factor from Figure C to Figure A? ii. Use the scale factor to describe how the perimeter and area of Figure A are related to the perimeter and area of Figure C. iii. Write a coordinate rule of the form (mx, my) that can be used to find the coordinates of any point of Figure A from the corresponding points of Figure C.
8 10. What is the scale factor from an original figure to its image if the image is made using the given method? a. A two-rubber-band stretcher b. A copy machine with size factor 150% c. A copy machine with size factor 250% d. The coordinate rule (0.75x, 0.75y) 11. a. Use the polygons below. Which pairs of polygons are similar figures? b. For each pair of similar figures, list corresponding sides and angles. c. For each pair of similar figures, find the scale factor that relates side lengths of the larger figure to the corresponding side lengths of the smaller figure.
9 12. On grid paper, draw a rectangle a rectangle with an area of 14 square centimeters. Label it ABCD. a. Write and use a coordinate rule that will make a rectangle similar to rectangle ABCD that is three times as long and three times as wide. Label it EFGH. b. How does the perimeter of rectangle EFGH compare to the perimeter of rectangle ABCD? c. How does the area of rectangle EFGH compare to the area of rectangle ABCD? d. How do your answers to part (b) and (c) relate to the scale factor from rectangle ABCD to rectangle EFGH? 13. A student drew the figures below. The student says that two shapes are similar because there is a common scale factor for all the sides. The sides of the figure on the right are twice as long as those of the figure on the left. What do you say to the student to explain why the figures are not similar?
Coordinates of Characters. c. Which of the new characters (Glum, Sum, Tum, and Crum) are members of the Wump family, and which are impostors?
Applications 1. This table gives key coordinates for drawing the mouth and nose of Mug Wump. It also gives rules for finding the corresponding points for four other characters some members of the Wump
Coordinates of Characters Mug Wump Glum sum Tum Crum Rule (x, y) (1.5x, 1.5y) (3x, 2y) (4x, 4y) (2x, y) Nose (Start Over)
A C E Applications Connections Extensions Applications 1. The table below gives key coordinates for drawing Mug Wump s mouth and nose. It also gives rules for finding the corresponding points for four
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